trig integrals involving secant and tangent (calculus 2)

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Күн бұрын

In this calculus tutorial, we will be doing 8 integrals involving secant and tangent. Be sure to use the trig identities accordingly.
0:00 Integral of tan^3(x)
1:34 integral of sec^6(x)
4:20 integral of tan^2(x)*sec^6(x)
6:44 integral of tan(x)*sec^3(x)
8:02 integral of tan^3(x)*sec(x)
9:44 integral of 1/sec(x)
10:17 integral of (sec(x)+tan(x))^2
11:44 integral of sec^3(x)
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Пікірлер: 23

@puddleduck1405 Жыл бұрын

I used to struggle so much with these kind of integrals, I never knew when to use u=secx and when to do u=tanx. I have a really good understanding of this now! Thank you, and God bless you

@petereziagor4604 2 жыл бұрын

So, I used KZfaq search to look for the integral of secx dx and I saw your video from six years ago It was really nice 🙌

@salaheddinemath272 2 жыл бұрын

Thanks for your help

@mathsandsciencechannel 2 жыл бұрын

Nice solution

@searacha5604 2 жыл бұрын

This is so easy to understand. Thank you!

@lanomusambazi8654 2 жыл бұрын

Suppose secant has an odd power, how do we integrate such?

@ShinyTreecko 9 ай бұрын

At 7:32, during the U sub operation why do we transform only the sec^2(x) into U? If we made U == sec(x) then wouldn't the other "sec(x)" in the integral also become a u? Shouldn't the equation be "(U^2) * (U) * (tan(x)) " divided by du, sec(x)tan(x). I am probably over thinking this, but I've had this question since I started doing trig integrals.

@Eng586 3 ай бұрын

When doing u sub you can choose what you want to set as u, as long as it helps you integrate it. In this case he only chose sec^2x because if you do u sub du=secxtanx which cancels out the other part and leaves you with something you can integrate easily (u^2)

@theepicfailguy127 2 жыл бұрын

In the first can't we just let u as tanx and then integrate u^3 and tanx and multiply them

@Nikitashm 6 ай бұрын

i love you havent even watched the video yet

@udaysrivastava1957 2 жыл бұрын

I have a problem for question 1. integral tanx sec²x dx you wrote it as (tan²x)/2 but it can also be (sec²x)/2 But if both are the same then tan²x = sec²x tan x = sec x which means x is (1/2) (4nπ + π) Why are we getting the values of x??

@bprpcalculusbasics 2 жыл бұрын

Yea. That’s called “off by a constant”. I have an old video explaining it in details.

@lanomusambazi8654 2 жыл бұрын

Mmmmm no I don't agree to this.

@getezra1 Жыл бұрын

on prob 1 if we take u = sec x, and rewrite tanxset^2x as tanxsecx.secx then du/dx = secxtanx which will workout seamlessly afterwards. (just optional)

@mathevengers1131 2 жыл бұрын

Giraffe has learned all that now.

@mathevengers1131 2 жыл бұрын

@@aashsyed1277 yeah but less than before.

@mathevengers1131 2 жыл бұрын

@@aashsyed1277 Rising Star Math KZfaqres Challenge

@mr.ahlaguchiha2770 2 жыл бұрын

1:17 min Mistake spotted 🥸, integrale of tan x isn t ln sec x actually it is ln cos x . since secx equal to 1/cosx

@ital3nt3d Жыл бұрын

Little late, but for anyone needing clarification on this in the future: the integral of tanx is indeed -lncos x, but the in the case of this video in problem 1, we arent finding the integral of tan x per se and using u-sub instead. What i mean is we let u = secx, du = secx tanx dx, thus dx = 1/secx tan x....but dont forget to replace the secx in the dx we calculated with u. So dx=1/u tanx. If you then replace dx in our original setup and replace secx with u: (u^2-1)tanx * (1/u tanx). Tanx cancels out and we get (u^2-1)/u. Rewrite as (u^2/u)-(1/u) and simplify to get u - (1/u) and thus the integral of this would be (u^2/2)-ln(|u|), replace the u's for sec x and we get the final answer (sec^2x/2) - ln|secx|. Hope that helps.

@puddleduck1405 Жыл бұрын

nope he's right. the tan(x) is sin(x)/cos(x). the derivative of cos(x) is MINUS sin(x). so the integral of tan(x) is -ln(cosx). Then using log rules, we can bring the minus up, so that it is ln(1/cosx) which is ln(secx).

@puddleduck1405 Жыл бұрын

@@ital3nt3d nah bro u said the integral of tanx is ln cosx. its not. it is -ln(cosx). which is the same as ln(secx) using log rules :)

@ital3nt3d Жыл бұрын

@moonlight_studies hey. You're right it was a typo and I fixed it. The final form of the answer was correct tho with the negative being present. I don't really remember any of this tbh lmao but point of my comment was to further explain the steps used to show that a mistake wasn't made by the video (as per the original comment). Granted I'm just another student so could wrong but the work made sense at the time and I asked on chegg and symbolab at a later point. Gl!

@puddleduck1405 Жыл бұрын

@@ital3nt3d haha no worries, Gl! :D